1997grand voyager is blowing cold air new thermostate water pump and the raditor and heater core has been back flushed it started blowing hot air again then went back to blowing cold air again

Could be an air lock in the hot water system.
Normal procedure is to slacken a hose clip at the highest point and bleed the air out.
Don't try this when the engine is hot or someone could get scalded. Surprised the dealer didn't bleed the system as they would have a special radiator cap that allows the system to be put under pressure

Try flushing the heater core.You know the hose they can reach operating temperature,but sometimes the core itself is just plugged

Flush coolant system out first with prestone or peak coolant flush if problem still exist replace heater core.

Thermostat.? if you haven't? Do it first then try it. While the car is running for a while touch the heater hoses that lead to the firewall. if one is cold and one is hot? You have a blocked Heater core. Follow the hoses back to the engine. Unconnect them both. By using a garden hose flush out the heater core do one side and then reverse by doing the other hose Lots of junk will come out so be care ful. Mistake people make is "Flushing the system" That doesn't mean your flushing the heater core.
Seeing that you have done everything else it could be the thermostat which you didn't list or the heater core being clogged. When you finished installing the thermostat and flushing the heater core out. Replenish the coolant system . If you have a bleeder on the thermostat housing? use it . loosen it and top off the fluid until you see fluid comeout of the bleeder. The system being air bound would cause no heat..

flush heater core if one hose is hot and one cold there is blockage in heater core back flushing heater core should fix problem

Try removing the Heater hoses from heater tubes(be careful not to break heater tubes off) then back flush heater core with garden hose(Don't use a lot of pressure). Jell from antifreeze builds up in the heater core and blocks the coolant flow. If it is easier, remove the heater hoses from the engine, that is safer. Back flush the heater from the hoses. To Back Flush (The hose coming from the water pump is the inlet)(Hose going to Manifold is outlet) Back flush outlet hose! To much water pressure may cause damage to heater core!!!! Do Not ues AIR!!!!

Need more information. The most important thing would be to watch the heater water valve move when someone turns the control from hot to cold, back and forth?
Heater valve controls tend to be operated by vacuum, and switched by a heater computer. Lots of possibilities. But first tell us what you see move when operated? Valve is usually in engine compartment, in the heater hose. Follow the hot one.

sounds like your either low on coolant or a possible blown head gasket, the head gasket will create too much pressure in the cooling system and blow your coolant out of the overflow and fill the heater core with air causing the heater to be cold or your just low on coolant due to a leak or improperly filled cooling system. so fill the cooling system resovoir while vehicle is running while keeping the level at "full hot" line until the fans have come on and gone back off (a/c and defrost must be off) then drive on the interstate until the heater gets hot. if the vehicle tries to push the coolant out while filling the system headgasket is a definite possibilty. BE CAREFUL COOLANT GETS HOT!!!

First you have to identify what causes the problem.
To do this you have to:
1) When engine is cold check the level of coolant. If it is low fill it up.
2) Start engine and check if engine reaches regular temperature. If your engine is not heated enough it means your thermostat does not work properly and should be replaced.
3) If engine temperature is normal, then check the temperature of pipes that go to/from heater core. These pipes are located up the fire wall (easier access is from the passenger side). If pipe/pipes are cold (even engine is worm) it means you heater core is plugged and should be flushed. Keep in mind, flushing the whole cooling system is different from flushing heater core.
4) If pipe/pipes are hot/warm, turn off the fan, switch controller to the hot position, wait for 3-4 minutes and turn on the fan. Note if the cold air blows first or warm air blows first but it cools down in 5-10 seconds. If the air blows cold than it is most probably the problem with blend door or blend door actuator.
5) If air blows warm first and then cools down, then while running engine and remaining the transmission in PARKING position, press on the gas pedal until your engine reaches 3,000 RPM. Check if your heater blows warm/hot air. If it does, then your water pump does not work properly and should be replaced. If the air still cold, I would suggest to flush the heater core.

have you flushed out the radiator ? get some radiator flush and flush it out. There could be a blockage in the radiator.